A one-dimensional model of 3-D structure for large deformation: a general higher-order rod theory
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A higher-order one-dimensional model in a curvilinear cylindrical coordinate system and associated finite element model are presented. A general displacement field of the cross section of the rod or the structures in the polar coordinate system is assumed, and the associated governing equation of motion in the Lagrangian frame of reference is derived. Since the displacement field considered is very general, the theory is not limited to rods but can be used to analyze thick, solid, or hollow arbitrary cross section members or a shell structure whose axis can be given as a space curve. A nonlinear finite element model of the theory which can model large deformation is developed. Numerical examples are presented to illustrate the usefulness and accuracy of the model in analyzing shell structures (e.g., spiral duct), whose central axis is a space curve, subjected to point loads and internal or external pressure.
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